This is a first competitive renewal of a Program Project Grant with the goal of developing experimental and computational tools of cryo-electron microscopy in the context of a widening range of biological applications. Atomic resolution pictures of complex assemblies are the ultimate objectives. The renewal has three central themes. The first is a focus on membrane proteins and membrane-associated assemblies. We will expand work from the first grant period on 2-D membrane protein crystals, on clathrin-coated vesicles, and on single particle analysis as applied to membrane proteins. The second theme is development of maximum likelihood methods in single-particle reconstructions, with the goal of extending our ability to obtain molecular structural information from conformationally heterogeneous specimens. The results of the previous grant period demonstrate that x-ray crystallography and cryo-EM form a smooth continuum of methods that indeed can achieve atomic resolution for a great variety of homogeneous samples. The goal is now to improve the robustness of single-particle reconstruction algoirthms and to deal with conformationally heterogeneous single particles. Cryo-electron tomography of macromolecular complexes will also have a role in bridging between lower resolution analyses of the assemblies and high-resolution analyses of their substructures. The third theme is precisely the application of these methods to transient, multi-state assemblies, such as spliceosomes and kinetochore substructures. Relevance: Each of the assemblies we study has an important connection with a human disease, as outlined in each of the project sections. More generally, "molecular machines", rather than single enzymes, will be targets of future interventions, and learning how to relate structure and function of such assemblies will underlie such translational developments.